Put simply, DTS-HD Master Audio (also known as DTS-Master) is the high definition audio version of DTS. It is a completely lossless audio signal, so has not been compressed in anyway in order to fit it on a Blu-ray disc. This has only been possible since the introduction of the new Blu-ray and HD-DVD formats. The advantages are that that you will be getting the audio signal exactly as the film studio intended.
In order to use DTS-HD you will need a Blu-ray (or HD-DVD player) player that will either decode the signal into DTS-HD or send it as a raw bitstream output so an external amplifier can do the decoding. You will also need to send the signal by an HDMI cable (to at least the HDMI 1.3 specification, which most should be now). Then it is up to your speakers to do the job!
It is very similar to its rival sound format, Dolby TrueHD, which is also a lossless sound format. Both are well supported on bew HD capable equipment now.
See also our page on Dolby TrueHD.